In this paper, we present an algorithm to estimate a signal from its modified short-time Fourier transform (STFT). This algorithm is computationally simple and is obtained by minimizing the mean squared error between the STFT of the estimated signal and the modified STFT. Using this algorithm, we also develop an iterative algorithm to estimate a signal from its modified STFT magnitude. The iterative algorithm is shown to decrease, in each iteration, the mean squared error between the STFT magnitude of the estimated signal and the modified STFT magnitude. The major computation involved in the iterative algorithm is the discrete Fourier transform (DFT) computation, and the algorithm appears to be real-time implementable with current hardware technology. The algorithm developed in this paper has been applied to the time-scale modification of speech. The resulting system generates very high-quality speech, and appears to be better in performance than any existing method.

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Signal estimation from modified short-time Fourier transform

a dissertation submitted to the department of music and the committee on graduate studies of stanford university in partial fulfillment of the requirements for the degree of doctor of philosophy This dissertation introduces a new analysis/synthesis method. It is designed to obtain musically useful intermediate representations for sound transformations. The method's underlying model assumes that a sound is composed of a deterministic component plus a stochastic one. The deterministic component is represented by a series of sinusoids that are described by amplitude and frequency functions. The stochastic component is represented by a series of magnitude-spectrum envelopes that function as a time-varying filter excited by white noise. Together these representations make it possible for a synthesized sound to attain all the perceptual characteristics of the original sound. At the same time the representation is easily modified to create a wide variety of new sounds. This analysis/synthesis technique is based on the short-time Fourier transform (STFT). From the set of spectra returned by the STFT, the relevant peaks of each spectrum are detected and used as breakpoints in a set of frequency trajectories. The deterministic signal is obtained by synthesizing a sinusoid from each trajectory. Then, in order to obtain the stochastic component, a set of spectra of the deterministic component is computed, and these spectra are subtracted from the spectra of the original sound. The resulting spectral residuals are approximated by a series of envelopes, from which the stochastic signal is generated by performing an inverse-STFT. The result is a method that is appropriate for the manipulation of sounds. The intermediate representation is very flexible and musically useful in that it offers unlimited possibilities for transformation. iii iv To Eva and Octavi v vi Acknowledgements I wish to thank my main advisor Prof. John Chowning for his support throughout the course of this research. Also thanks to Prof. Julius Smith without whom this disserta-tion could not have even been imagined. His teachings in signal processing, his incredible enthusiasm, and practically infinite supply of ideas made this work possible. I have to acknowledge Prof. Earl Schubert for always being ready to help with the most diverse problems that I have encountered along the way.

A system for sound analysis/transformation/synthesis based on a deterministic plus stochastic decomposition

The goal of this paper is to develop fast algorithms for signal reconstruction from magnitudes of frame coefficients. This problem is important to several areas of research in signal processing, especially speech recognition technology, as well as state tomography in quantum theory. We present linear reconstruction algorithms for tight frames associated with projective 2-designs in finite-dimensional real or complex Hilbert spaces. Examples of such frames are two-uniform frames and mutually unbiased bases, which include discrete chirps. The number of operations required for reconstruction with these frames grows at most as the cubic power of the dimension of the Hilbert space. Moreover, we present a very efficient algorithm which gives reconstruction on the order of d operations for a d-dimensional Hilbert space.

/pdf/painless-reconstruction-from-magnitudes-of-frame-28q3k2bl47.pdf

Painless Reconstruction from Magnitudes of Frame Coefficients

https://maxwell.ict.griffith.edu.au/spl/publications/papers/spcom05_phase.pdf

On the usefulness of STFT phase spectrum in human listening tests

In this paper a new speech analysis/synthesis technique is presented which provides the basis for a general class of speech transformations including time-scale modification, frequency scaling, and pitch modification. These modifications can be performed with a time-varying change, permitting continuous adjustment of a speaker's fundamental frequency and rate of articulation. The method is based on a sinusoidal representation of the speech production mechanism which has been shown to produce synthetic speech that preserves the wave-form shape and is perceptually indistinguishable from the original. Although the analysis/synthesis system was originally designed for single-speaker signals, it is also capable of recovering and modifying nonspeech signals such as music, multiple speakers, marine biologic sounds, and speakers in the presence of interferences such as noise and musical backgrounds.

http://ieeexplore.ieee.org/iel6/8361/26343/01168380.pdf

Speech Traneformatione Based on a Sinusoidal Representation

This paper presents various conditions that are sufficient for reconstructing a discrete-time signal from samples of its short-time Fourier transform magnitude. For applications such as speech processing, these conditions place very mild restrictions on the signal as well as the analysis window of the transform. Examples of such reconstruction for speech signals are included in the paper.

Signal reconstruction from the short-time Fourier transform magnitude

Major artifacts of the spectral subtraction signal restoration technique are the presence of harmonic patterns and blurring effects for images, and the presence of short tone bursts of varying frequency for speech signals. In this paper, we discuss several techniques developed to reduce these artifacts. Examples are shown to illustrate the performance of these techniques.

Improved spectral subtraction for signal restoration

Arithmetic concurrencies, such as those found in special-purpose fast Fourier transform (FFT) hard-ware, are surveyed and categorized. Similar structures are then derived for the Winograd Fourier transform algorithm (WFTA). Relative time-efficiency plots are obtained for the 1024-point radix-4 FFT and the 1008-point WFTA as a function of the number of real arithmetic operations executable in parallel. This comparison shows that the relative time efficiency of the two algorithms in sequential computations generally carries over to cases where arithmetic parallelism is exploited.

H. Nawab

Papers

Signal reconstruction from the short-time Fourier transform magnitude

Improved spectral subtraction for signal restoration

Parallelism in the computation of the FFT and the WFTA